Nucleation in Nonequilibrium Hypersonic Flow: Theory and Optical Diagnostics

The operating range of supersonic and hypersonic ground facilities is often limited at low temperature by the liquefaction of the working gas through the nucleation of molecular clusters. Because properties of molecular clusters differ appreciably from those of bulk liquids, accurate evaluation of the cluster free energy is the primary challenge in nucleation modeling. In hypersonic facilities in which nucleation occurs at high stagnation temperature, the flow is often in a thermal nonequilibrium state and vibrationally excited molecules may interact with nucleating molecular clusters. A semi-empirical density gradient theory (SEDGT) is developed by regarding the molecular cluster as an inhomogeneous fluid, with free energy density a function of both the local number density and the magnitude of the density gradient. The unknown parameter of the model is obtained in a self-consistent manner by comparison to experimental values for surface tension and nucleation rate. The cluster density profile, free energy barrier, and surface tension are then evaluated. Reduced order models for the cluster free energy barrier and nucleation rate are reviewed, and the quasi-steady nucleation rate of molecular clusters in a supersaturated gas is presented. The set of kinetic equations describing the growth and decay of molecular clusters are written and amalgamated for numerical solution. Models for cluster growth are coupled to the conservation of mass, momentum, and energy for a condensable ideal gas. Simulation results for the nucleation of N2 and CO2 in supersonic and hypersonic nozzles are compared to experimental data obtained from available literature and from experiments conducted at a Mach 4 blowdown wind tunnel using laser Rayleigh scattering gas density measurements. It is found that the modeled condensation onset of N2 using SEDGT is in good agreement with experiment. Interaction of molecular clusters with vibrationally excited molecules in a nonequilibrium population are considered in predictions of condensation onset for large quiet Mach 6 and Mach 10 tunnels under development. A coherent anti-Stokes Raman spectroscopy (CARS) diagnostic setup is developed for the study of nucleation in thermal nonequilibrium flow. Low vibrational temperature measurements of nitrogen are performed in Mach 2 flow by collinear CARS using a noncollinear optical parametric oscillator with narrow bandwidth Stokes beam and nonresonant background suppression. In Mach 2 flow with a stagnation temperature of 800 K, best-fit synthetic nonequilibrium spectra indicate a vibrational temperature of 790 K, which is about 340 K higher than the rotational temperature, indicating thermal nonequilibrium.